Question

If 2 $\left(\begin{array}{l l }3 & 4 \\ 5 & x\end{array}\right)$ + $\left(\begin{array}{l l }1 & y \\ 0 & 5\end{array}\right)$ = $\left(\begin{array}{l l }7 & 0 \\ 10 & 5\end{array}\right)$ find x - y.

Evaluate $\textstyle\int\!{\frac{(1+\log x)^{2}}{x}}\,d x\,.$

If A is a square matrix such that A² = A, then write the value of (I + A)² – 3A.

Write value of $\textstyle\int$ sec x(sec x + tan x) dx

Let f : R → R be defined by f(x) = 3x² – 5 and g : R → R be defined by g(x) =${\frac{x}{x^{2}+1}}.$ find gof(x) .

Write the value of $\textstyle\int\!{\frac{\ d x}{x^{2}+16}}$

If A = $\left(\begin{array}{l l l }1 & 2 & 2 \\ 2 & 1 & x \\ -2 & 2 & -1\end{array}\right)$ is a matrix satisfying AA’ = 9I, find x.